{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:46:13Z","timestamp":1760240773821,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,9,12]],"date-time":"2019-09-12T00:00:00Z","timestamp":1568246400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["No.2016YFB0800401"],"award-info":[{"award-number":["No.2016YFB0800401"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 61532020, 61671161"],"award-info":[{"award-number":["No. 61532020, 61671161"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, the security analysis of an image chaotic encryption algorithm based on Latin cubes and bit cubes is given. The proposed algorithm adopts a first-scrambling-diffusion- second-scrambling three-stage encryption scheme. First, a finite field is constructed using chaotic sequences. Then, the Latin cubes are generated from finite field operation and used for image chaotic encryption. In addition, according to the statistical characteristics of the diffusion image in the diffusion stage, the algorithm also uses different Latin cube combinations to scramble the diffusion image for the second time. However, the generation of Latin cubes in this algorithm is independent of plain image, while, in the diffusion stage, when any one bit in the plain image changes, the corresponding number of bits in the cipher image follows the change with obvious regularity. Thus, the equivalent secret keys can be obtained by chosen plaintext attack. Theoretical analysis and experimental results indicate that only a maximum of     2.5 \u00d7   w \u00d7 h  3  + 6     plain images are needed to crack the cipher image with     w \u00d7 h     resolution. The size of equivalent keys deciphered by the method proposed in this paper are much smaller than other general methods of cryptanalysis for similar encryption schemes.<\/jats:p>","DOI":"10.3390\/e21090888","type":"journal-article","created":{"date-parts":[[2019,9,12]],"date-time":"2019-09-12T10:56:06Z","timestamp":1568285766000},"page":"888","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["On the Security of a Latin-Bit Cube-Based Image Chaotic Encryption Algorithm"],"prefix":"10.3390","volume":"21","author":[{"given":"Zeqing","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Automation, Guangdong University of Technology, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Simin","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Automation, Guangdong University of Technology, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/s11071-018-4056-x","article-title":"Brief review on application of nonlinear dynamics in image encryption","volume":"92","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/s11760-009-0114-7","article-title":"Video watermarking using wavelet transform and tensor algebra","volume":"4","author":"Abdallah","year":"2010","journal-title":"Signal Image Video Process."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Kamel, M., and Campilho, A. (2007). MPEG Video Watermarking Using Tensor Singular Value Decomposition. Image Analysis and Recognition, Springer.","DOI":"10.1007\/978-3-540-74260-9"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wang, J., and Ding, Q. (2018). Dynamic Rounds Chaotic Block Cipher Based on Keyword Abstract Extraction. Entropy, 20.","DOI":"10.3390\/e20090693"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1007\/s11071-010-9749-8","article-title":"A chaotic image encryption algorithm based on perceptron model","volume":"62","author":"Wang","year":"2010","journal-title":"Nonlinear Dyn."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.asoc.2014.09.039","article-title":"A new image encryption algorithm based on non-adjacent coupled map lattices","volume":"26","author":"Zhang","year":"2015","journal-title":"Appl. Soft. Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.optlaseng.2014.08.005","article-title":"A novel chaotic block image encryption algorithm based on dynamic random growth technique","volume":"66","author":"Wang","year":"2015","journal-title":"Opt. Lasers Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3320","DOI":"10.1016\/j.camwa.2010.03.017","article-title":"Color image encryption based on one-time keys and robust chaotic maps","volume":"59","author":"Liu","year":"2010","journal-title":"Comput. Math. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3895","DOI":"10.1016\/j.optcom.2011.04.001","article-title":"Color image encryption using spatial bit-level permutation and high-dimension chaotic system","volume":"284","author":"Liu","year":"2011","journal-title":"Opt. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6954","DOI":"10.3390\/e17106954","article-title":"A Novel Image Encryption Algorithm Based on DNA Encoding and Spatiotemporal Chaos","volume":"17","author":"Song","year":"2015","journal-title":"Entropy"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.sigpro.2018.09.029","article-title":"A color image cryptosystem based on dynamic DNA encryption and chaos","volume":"155","author":"Chai","year":"2019","journal-title":"Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1016\/j.asoc.2012.01.016","article-title":"Image encryption using DNA complementary rule and chaotic maps","volume":"12","author":"Liu","year":"2012","journal-title":"Appl. Soft. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.optlaseng.2015.03.022","article-title":"A novel chaotic image encryption scheme using DNA sequence operations","volume":"73","author":"Wang","year":"2015","journal-title":"Opt. Lasers Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/j.ins.2019.02.049","article-title":"Fast image encryption algorithm based on parallel computing system","volume":"486","author":"Wang","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.ins.2019.08.041","article-title":"Image encryption algorithm for synchronously updating Boolean networks based on matrix semi-tensor product theory","volume":"507","author":"Wang","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.optlaseng.2016.10.019","article-title":"Color image encryption based on hybrid hyper-chaotic system and cellular automata","volume":"90","author":"Moattar","year":"2017","journal-title":"Opt. Lasers Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1016\/j.image.2016.12.007","article-title":"An image encryption algorithm based on the memristive hyperchaotic system, cellular automata and DNA sequence operations","volume":"52","author":"Chai","year":"2017","journal-title":"Signal Process.-Image Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.optlaseng.2018.11.010","article-title":"A color image encryption algorithm based on Hopfield chaotic neural network","volume":"115","author":"Wang","year":"2019","journal-title":"Opt. Lasers Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1016\/j.compeleceng.2011.11.019","article-title":"A robust hybrid method for image encryption based on Hopfield neural network","volume":"38","author":"Bigdeli","year":"2012","journal-title":"Comput. Electr. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2018.11.010","article-title":"A novel image cipher based on 3D bit matrix and latin cubes","volume":"478","author":"Xu","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1016\/j.ijleo.2018.06.112","article-title":"A novel image encryption algorithm based on self-orthogonal Latin squares","volume":"171","author":"Xu","year":"2018","journal-title":"Optik"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1007\/s11071-015-2057-6","article-title":"An efficient image encryption scheme using lookup table-based confusion and diffusion","volume":"81","author":"Chen","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.ins.2014.02.156","article-title":"A symmetric image encryption algorithm based on mixed linear\u2013nonlinear coupled map lattice","volume":"273","author":"Zhang","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"47102","DOI":"10.1109\/ACCESS.2018.2867111","article-title":"Cryptanalyzing a Color Image Encryption Scheme Based on Hybrid Hyper-Chaotic System and Cellular Automata","volume":"6","author":"Li","year":"2018","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wen, H., Yu, S., and L\u00fc, J. (2019). Breaking an Image Encryption Algorithm Based on DNA Encoding and Spatiotemporal Chaos. Entropy, 21.","DOI":"10.3390\/e21030246"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1016\/j.sigpro.2010.09.014","article-title":"Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks","volume":"91","author":"Li","year":"2011","journal-title":"Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1109\/TIFS.2015.2489178","article-title":"On the Security of Permutation-Only Image Encryption Schemes","volume":"11","author":"Jolfaei","year":"2016","journal-title":"IEEE Trans. Inf. Forensic Secur."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"12584","DOI":"10.1109\/ACCESS.2019.2893760","article-title":"Cryptanalysis and Improvement of the Image Encryption Scheme Based on 2D Logistic-Adjusted-Sine Map","volume":"7","author":"Feng","year":"2019","journal-title":"IEEE Access"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.ins.2016.01.017","article-title":"Image encryption using 2D Logistic-adjusted-Sine map","volume":"339","author":"Hua","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.1109\/TCSVT.2014.2369711","article-title":"Design and ARM-Embedded Implementation of a Chaotic Map-Based Real-Time Secure Video Communication System","volume":"25","author":"Lin","year":"2015","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1850086","DOI":"10.1142\/S0218127418500864","article-title":"Cryptanalysis of a Chaotic Stream Cipher and Its Improved Scheme","volume":"28","author":"Lin","year":"2018","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.1007\/s11071-016-3311-2","article-title":"Cryptanalysis of a chaotic image cipher using Latin square-based confusion and diffusion","volume":"88","author":"Hu","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1016\/j.sigpro.2017.11.005","article-title":"Cryptanalysis and enhancements of image encryption using combination of the 1D chaotic map","volume":"144","author":"Wang","year":"2018","journal-title":"Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.sigpro.2017.03.011","article-title":"A new color image encryption using combination of the 1D chaotic map","volume":"138","author":"Pak","year":"2017","journal-title":"Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.sigpro.2017.06.014","article-title":"Cryptanalysis and enhancements of image encryption based on three-dimensional bit matrix permutation","volume":"142","author":"Wu","year":"2018","journal-title":"Signal Process."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.sigpro.2015.06.008","article-title":"Image encryption based on three-dimensional bit matrix permutation","volume":"118","author":"Zhang","year":"2016","journal-title":"Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1016\/j.sigpro.2011.10.023","article-title":"A novel colour image encryption algorithm based on chaos","volume":"92","author":"Wang","year":"2012","journal-title":"Signal Process."},{"key":"ref_38","first-page":"288","article-title":"Latin k-cubes","volume":"12","author":"Arkin","year":"1974","journal-title":"Fibonacci Q."},{"key":"ref_39","first-page":"553","article-title":"On the solution of algebraic equations over finite fields","volume":"10","author":"Berlekamp","year":"1967","journal-title":"Inf. Comput."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/9\/888\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:19:32Z","timestamp":1760188772000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/9\/888"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,12]]},"references-count":39,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2019,9]]}},"alternative-id":["e21090888"],"URL":"https:\/\/doi.org\/10.3390\/e21090888","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2019,9,12]]}}}